Dr. McDonald's Mathematics Course Blog
Here are a few questions to look at that involve applications of the new techniques and results (the chain rule, the product rule, and derivatives of exponential functions) we’re recently covered.
Make sure to start these before our next lesson, and aim to have them completed by Monday.
Pages 715–716 questions 3, 7, 9, 11
Pages 728 questions 1 a b e h i, 4, 6, 9, 10
Attached is a set of questions that you can use to practice the chain rule. We can look at the answers in our lesson tomorrow.
Welcome back for Year 13, and our second year of Mathematics HL!
This year we’ll be in Mathematics 12, in the Mathematics Corridor (formerly the English Corridor—our room was formerly Ms Donnelly’s room), and our first lesson will be Sunday, Lesson 5.
Ready?
Attached below are the final review notes for the summer.
Derivatives Review Notes (Complete)
Again, this document contains all prior review notes, so you won’t need to refer to the earlier versions when working through this material.
The newly added sections focus on using the graph of the derivative (and the second derivative) to discover features of the graph of the original function, as in applications of Calculus it’s often the case that we understand more about the derivative than we do about the original function.
Also included below is your assignment, due on the 29th of August (your second day back). I’ve marked the last two questions (4 and 5) with a star, as they are optional (though I would strongly encourage you to do those as well). As always, post any questions below!
Hope you’re all enjoying the break!
Attached below is the second part of your summer review notes on the derivative (note that the document attached below contains the previous review notes as well). Again, some of this material will be review from the last few lessons, but there are a few new elements that you should get acquainted with now, and which we’ll be spending more time with at the start of next term.
Also as before, there are some questions at the end of the new section that you should complete (but which will not be collected at the start of the term). If you have any trouble with these, please do post your questions in the comments section below.
There will be one final set of additional notes (again, focused on review from the last few lessons), which will be posted, along with your short summer assignment, sometime on or before the 7th of August.
Derivatives Review Notes (updated)
Over the summer I’ll be posting a few review notes, and (later in July) a short assignment for you to complete for the end of the summer. The first topic for review is the definition of the derivative.
I suggest that you read through the attached notes and complete the questions in each section. (Your answers to the questions included in the note will not be collected, but you really must complete them in order to best understand this material.) Note that there are no diagrams included in these notes, and I suggest that you create your own supplemental diagrams as you’re reading through the material.
As always, post any questions you have in the comments section below, or send them to me in an email if you’d prefer.
Complete the following question for tomorrow’s lesson.
Use the derivative of the function \[f(x)=x^3-x^2+2x-1\] to find the coordinates of the (local) extrema of \(f\).
Update: Oops! The function above has no extrema! (How can you tell from the first derivative?) However, it does have what’s called a point of inflexion, which is a point at which the function changes concavity (from concave up to concave down, or vice versa). Can you find the coordinates of the point of inflexion?
At any rate, the function \(g\) below does have extrema, so you should find the coordinates of the extrema of \(g\). Can you also find the coordinates of its point of inflexion?
\[g(x)=x^3-x^2-2x-1\]
This was going to be part of a test, but instead let’s use the questions below for an assignment. Have this completed and ready to hand in by Wednesday this week. Electronic submissions are accepted, but not required.
Below is the slide of questions we began today. Complete these for our lesson tomorrow.
I’ve added a new resource to the HL Resources page that will be useful when studying. Note that (as with the resources you’ve already got), you will be able to find past paper questions that will be especially useful when studying for our end-of-year exam.